Wobbly gear ring needs fixing
I tried the following method with some success.  It's tedious and not very precise, but hopefully someone posts a better solution. 

In EDIT mode and viewing ring gear along its profile so it appears as a straight line, I slowly rotated it. Whenever I noticed the profile getting 'thicker,' this indicated a 'wobble' where the opposing arcs are not aligned because the circle is slightly skewed along its axis of rotation at that point. I then adjusted the rotation along the perpendicular axis until the profile narrowed or thinned.

These adjustments need to be made in edit mode so they are applied in object mode.